An Optimization Problem with Volume Constrain for a Degenerate Quasilinear Operator
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چکیده
We consider the optimization problem of minimizing ∫ Ω |∇u| dx with a constrain on the volume of {u > 0}. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution u is locally Lipschitz continuous and that the free boundary, ∂{u > 0} ∩ Ω, is smooth.
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تاریخ انتشار 2008